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Hagrid
In trigonometry, the reciprocal of the function "tangent" is cotangent. If in the figure, tan B is given, then we can solve for the reciprocal of the angle. If tan B = 3/2 and the triangle is a right triangle, we can use the Pythagorean theorem mixed with trigonometric identities:

tan B = 3/2 
tan B = opposite / adjacent
opposite = 3
adjacent = 2

therefore, cot B = adjacent / opposite
then,
cot B = 2/3. 

We can only use this solution if the given triangle is a right triangle, if not, we may have to explore other solutions. 

The reciprocal of tanB is cotB which the ratio of the adjacent side and the opposite side.

In a right angle triangle tangent is the ratio of the opposite side to the adjacent side.Suppose a right angle triangle having sides adjacent a , opposite b and the hypotenuse b. Hence by the rules of trigonometry, we get,

[tex]TanB=\dfrac{opposite}{adjacent}[/tex]

[tex]TanB=\dfrac{b}{a}[/tex]

As it is known that the cotangent is the reciprocal of the tangent. Therefore,

[tex]TanB=\dfrac{1}{cotB}[/tex]

As the raciprocal of tanB is cot B. Therefore value of the raciprocal of tanB is,

[tex]cotB=\dfrac{1}{TanB}[/tex]

[tex]cotB=\dfrac{a}{b}[/tex]

Hence, the reciprocal of tanB is cotB which the ratio of the adjacent side and the opposite side.

For more about the trigonometry, follow the link below-

https://brainly.com/question/24236629

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